Alright, let's solve this problem step by step. We have 4496 and 7784 and we're adding them together.

Step 1: We'll start by adding the digits 6 & 4 in column 1 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 8 in column 2 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 4 & 7 in column 3 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 4 & 7 in column 4 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

So, 4496 + 7784 = 12280.

